Evolution of NLS with Bounded Data

MATHEMATICAL PICTURE LANGUAGE

Speaker:

Thomas Spencer - Institute for Advanced Study, Princeton

via Zoom Video Conferencing:  https://harvard.zoom.us/j/779283357

We study the nonlinear Schroedinger equation (NLS) with bounded initial data which
does not vanish at infinity. Examples include periodic, quasi-periodic and random initial data.
On the lattice we prove that solutions are polynomially bounded in time for any bounded data.
In the continuum, local existence is proved for real analytic data by a Newton iteration scheme.
Global existence for NLS with a regularized nonlinearity follows by analyzing a local energy norm.

This is joint work with B. Dodson and A. Soffer.